Question

Two lines, A and B, are represented by equations given below: Line A: y = x − 2 Line B: y = 3x + 4 Which of the following shows the solution to the system of equations and explains why? (1 point) a (−3, −5), because the point does not lie on any axis b (−3, −5), because the point satisfies both equations c (−4, −8), because the point satisfies one of the equations d (−4, −8), because the point lies between the two axes

Answer 1

Answer C. This point lies between the two axes and its coordinates satisfy both equations

Line A: y = x − 4

Line B: y = 3x + 4

Let's actually solve this system, using substitution:  Equate

Line A: y = x − 4   to   Line B: y = 3x + 4, obtaining:

                 x − 4  =     3x + 4

Subtract (x - 4) from both sides.  Doing so yields

                        0 = 2x + 8, and so x = -4.

From Line A let's find y:   Letting x = -4, we get:  y = -4 - 4 = -8

and so the solution is (-4, -8).  This matches Answer C. this point lies between the two axes and its coordinates satisfy both equations.